Facial Shape-from-Shading Using Principal Geodesic Analysis and Robust Statistics

  • William A. P. Smith
  • Edwin R. Hancock
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4647)


In this paper we make two contributions to the problem of recovering surface shape from single images of faces. The first of these is to develop a representation of the distribution of surface normals based on the exponential map, and to show how to model shape-deformations using principal geodesic analysis on the exponential map. The second contribution is to show how ideas from robust statistics can be used to fit the model to facial images in which there is significant self-shadowing. The method is evaluated on both synthetic and real-world images. It is demonstrated to effectively fill-in the facial surface when more than 30% of the area is subject to self-shadowing.


Median Absolute Deviation Facial Shape Cast Shadow Real World Image Light Source Direction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Zhao, W.Y., Chellappa, R.: Illumination-insensitive face recognition using symmetric SFS. In: Proc. CVPR, pp. 286–293 (2000)Google Scholar
  2. 2.
    Georghiades, A., Belhumeur, P., Kriegman, D.: From few to many: Illumination cone models for face recognition under variable lighting and pose. IEEE Trans. Pattern Anal. Mach. Intell. 23, 643–660 (2001)CrossRefGoogle Scholar
  3. 3.
    Prados, E., Faugeras, O.D.: Unifying approaches and removing unrealistic assumptions in shape from shading: Mathematics can help. In: Pajdla, T., Matas, J. (eds.) ECCV 2004. LNCS, vol. 3024, pp. 141–154. Springer, Heidelberg (2004)Google Scholar
  4. 4.
    Dovgard, R., Basri, R.: Statistical symmetric shape from shading for 3D structure recovery of faces. In: Pajdla, T., Matas, J. (eds.) ECCV 2004. LNCS, vol. 3022, pp. 99–113. Springer, Heidelberg (2004)Google Scholar
  5. 5.
    Blanz, V., Vetter, T.: A morphable model for the synthesis of 3D faces. In: Proc. SIGGRAPH, pp. 187–194 (1999)Google Scholar
  6. 6.
    Blanz, V., Vetter, T.: Face recognition based on fitting a 3D morphable model. IEEE Trans. Pattern Anal. Mach. Intell. 25, 1063–1074 (2003)CrossRefGoogle Scholar
  7. 7.
    Atick, J.J., Griffin, P.A., Redlich, A.N.: Statistical approach to SFS: Reconstruction of 3D face surfaces from single 2D images. Neural Comp. 8, 1321–1340 (1996)CrossRefGoogle Scholar
  8. 8.
    Smith, W., Hancock, E.R.: Recovering facial shape using a statistical surface normal model. In: Proc. ICIP (2005)Google Scholar
  9. 9.
    Blanz, V., Basso, C., Poggio, T., Vetter, T.: Reanimating faces in images and video. In: Proce. EUROGRAPHICS, pp. 641–650 (2003)Google Scholar
  10. 10.
    Fletcher, P.T., Joshi, S., Lu, C., Pizer, S.M.: Principal geodesic analysis for the study of nonlinear statistics of shape. IEEE Trans. Med. Imaging 23, 995–1005 (2004)CrossRefGoogle Scholar
  11. 11.
    Pennec, X.: Probabilities and statistics on riemannian manifolds: A geometric approach. Technical Report RR-5093, INRIA (2004)Google Scholar
  12. 12.
    Mardia, K.V., Jupp, P.E.: Directional Statistics. John Wiley and Sons Ltd., West Sussex (2000)zbMATHGoogle Scholar
  13. 13.
    Fisher, N.I.: Spherical medians. J. R. Statist. Soc. B 47, 342–348 (1985)zbMATHGoogle Scholar
  14. 14.
    Huber, P.: Robust Statistics. Wiley, Chichester (1981)zbMATHGoogle Scholar
  15. 15.
    Frankot, R.T., Chellappa, R.: A method for enforcing integrability in shape from shading algorithms. IEEE Trans. Pattern Anal. Mach. Intell. 10, 439–451 (1988)zbMATHCrossRefGoogle Scholar
  16. 16.
    USF HumanID 3D Face Database, Courtesy of Sudeep. Sarkar, University of South Florida, Tampa, FLGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • William A. P. Smith
    • 1
  • Edwin R. Hancock
    • 1
  1. 1.Department of Computer Science, The University of YorkUK

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